我想买一辆新车 is much more common and natural. But, the other expressions are also grammatically correct.

”我想买一辆新的车“语法上没错，但听着不自然，一般说”我想买辆新车“。

You can say 我想买新车 In Chinese we usually skip the classifier.

Thanks )

Yes. if both added are 2 characters long there is no need for a 的 The basic structure is build around 2 characters which gives usually an unambiguous meaning. If you were using 汽车 for car, the sentence should be 我想买一辆新 的 汽车 (because we have 3 characters) But I am simply, like you, a student. Chewing the big cake of learning Mandarin.